Phaseless near-field techniques from a random starting point

2020 ◽  
Author(s):  
Rocco Pierri ◽  
Giovanni Leone ◽  
Raffaele Moretta
Keyword(s):  
Near Field ◽  
Field Techniques ◽  
Starting Point ◽  
Random Starting Point

scholarly journals Manipulation of local optical properties and structures in molybdenum-disulfide monolayers using electric field-assisted near-field techniques

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Junji Nozaki ◽  
Musashi Fukumura ◽  
Takaaki Aoki ◽  
Yutaka Maniwa ◽  
Yohei Yomogida ◽  
...  
Keyword(s):  
Optical Properties ◽  
Electric Field ◽  
Molybdenum Disulfide ◽  
Near Field ◽  
Field Techniques

Optical contrast in near-field techniques

1995 ◽  
Vol 57 (2-3) ◽  
pp. 298-302 ◽  
Author(s):  
M.H.P. Moers ◽  
N.F. van Hulst ◽  
A.G.T. Ruiter ◽  
B. Bölger
Keyword(s):  
Near Field ◽  
Optical Contrast ◽  
Field Techniques

A beamforming paradox: Using far‐field techniques to design a near‐field microphone array

1997 ◽  
Vol 102 (5) ◽  
pp. 3208-3208
Author(s):  
Darren B. Ward ◽  
Rodney A. Kennedy ◽  
Thushara Abhayapala
Keyword(s):  
Microphone Array ◽  
Near Field ◽  
Far Field ◽  
Field Techniques

scholarly journals Probing plasmonic hot spots on single gold nanowires using combined near-field techniques

2015 ◽  
Author(s):  
Patrick Hsia ◽  
Ludovic Douillard ◽  
Fabrice Charra ◽  
Sylvie Marguet ◽  
Sergei Kostcheev ◽  
...  
Keyword(s):  
Hot Spots ◽  
Near Field ◽  
Gold Nanowires ◽  
Field Techniques

scholarly journals An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates

2003 ◽  
Vol 10 (9) ◽  
Author(s):  
Ivan B. Damgård ◽  
Gudmund Skovbjerg Frandsen
Keyword(s):  
Error Probability ◽  
Upper Bounds ◽  
Worst Case ◽  
Average Case ◽  
Closed Expression ◽  
Incremental Search ◽  
Starting Point ◽  
Primality Test ◽  
Algebraic Properties ◽  
Random Starting Point

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776^t for t iterations of the test in the worst case. EQFT extends QFT by verifying additional algebraic properties related to the existence of elements of order dividing 24. We also give bounds on the average-case behaviour of the test: consider the algorithm that repeatedly chooses random odd k bit numbers, subjects them to t iterations of our test and outputs the first one found that passes all tests. We obtain numeric upper bounds for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2^{-143} for k=500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicate that our test in the average case has the effect of 9 Miller-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point.

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